Singleton map – TheoremDex

▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Transitive set
▾ Ordinal number
▾ Cardinal number
▾ Set cardinality
▾ Singleton set
▾ Set of singletons

Singleton map

Formulation 0

Let $X$ and $Y$ each be a D11: Set such that

(i)	\begin{equation} \{ \{ x \} : x \in X \} \subseteq Y \end{equation}

The singleton map from $X$ to $Y$ is the D18: Map \begin{equation} X \to Y, \quad x \mapsto \{ x \} \end{equation}

Child definitions